DS7, who is HG+ and homeschooled (for those who don't know me yet), had a good day today. I wanted to share my glee with my buddies!

Just for fun, while we were still getting our books out of the car, I asked him a pre-algebra question that he was able to do in his head: x-3=7. Then he asked me about 3-x=7, which led to -x=4, and an excellent conversation about negative numbers and solving algebraic equations. That in turn led to a conversation about negative numbers and exponents, which led to a discussion about numbers so big that they're effectively infinity for normal human purposes--since he wanted to know what 2^100 was, and then he wrote some giganormous number to the gazillionth power. ("I have no idea what that is, kid! It's huge is what it is!" )

All of THAT led me to tell him the story of the grain of rice on day 1 doubled for every square on a chess board, and we figured that up as far as we cared to (Day 34 or so). Then we talked about rounding, since I did some as we did the math for 2^64. We even did part of a worksheet on rounding that I had printed from that site which someone suggested here on the forum. (I forget who. Sorry to space on the credit!)

All that great stuff took roughly 45 minutes. DS7 was busy and happy and learning the whole time. We flitted around a lot, but the kid can now round numbers no matter how big and to any place, he can multiply negative numbers now, and he can tell with one glance if a negative number with an exponent is + or -.

I call that a good math day! I love those! Happy, happy, joy, joy!

AWESOME

Seriously... I love those days. Thanks for sharing.

Hey, thanks for letting me share. It's so nice to have a place to enjoy those triumphs with people who get it and who don't think we're bragging or starting a "my kid is so smart" competition. Honestly, it just makes my heart feel light!

Yay, us! I love this forum!

That sounds like a terrific day, Kriston! It is just wonderful when learning is fun and exciting. It almost seems effortless then!

I second JB: Awesome!

What a great day. It reminds me of our dinner discussions. Now when we homeschool we don't have them as often as we used to Last winter DS6 spent lots of time calculating 2^ just for fun. I think he stopped around 2^70.

How is everything? How is it going without the babysitter? Still ready to send DS4 to K or are you hesitating a little bit. I overheard DS4 telling DS6 that once he is 5 he will be homeschooled as well

Yowsa, LMom! That's some serious persistence. We were estimating to only 4 places or so by the time we were in the millions, and we still only got to 2^34!

I'm impressed!

Yay! Sounds like a wonderful moment that could only happen while homeschooling, or in a very small class. Cool!

(of course, this sort of math stuff worries me, too, because i don't have much math ability myself, and I wouldn't be able to have that math moment with DS without some cramming on my part.)

So great! Really hammers home the idea that they will lead their learning!

SPG, you'd be surprised how much comes back to you. Honest!

I never considered myself very mathy either, and there will definitely come a time in the not-so-distant future when we either have to use a packaged math curriculum all the time, DH the engineer will have to take over teaching math, or DS7 will have to go back to some sort of school. But for now, it's actually kind of fun to wind our way through math as we like. I use Internet sites as guidance and worksheets, workbooks or computer games with him as they make sense. But as long as he's learning and enjoying it, I figure we're doing okay.

To tell you the truth, I'm probably *really learning* some of the concepts--not just the heuristics for getting an answer--for the first time, even though I got nearly all As in math all through school. It's not until you have to teach someone that you really understand something!

I do try to keep an eye on resources so that I don't teach him anything that's just plain wrong. If something comes up that I'm not sure about, I tell him so and we look it up. (There's value in seeing how to do that, too, I think.) But I don't cram. <shrug> It works so far. He's progressing, he's happy, and he's excited about learning, so we keep going!

I missed this, LMom. Sorry--I didn't mean to ignore you.

Things are good. I could have used a babysitter this week, but that's just because I was single parenting while DH was at a training. It's a temporary thing though. When he's been around to give me some backup, it has been fine to go without a sitter. The boys and I are all used to the routine now, and they play by themselves enough that I do okay. Plus I feel more relaxed about what we're doing, so I suspect I'm not wound quite as tightly as I was last year. That helps a lot.

Yes, we still plan to send DS4 to K next year. He adores his pre-K, which is apparently more academic this year than it was last year. (I didn't know that when I signed him up.) But he doesn't know how to read yet, so it seems to be hitting him where he is, so that's okay. I think K will be much the same.

Plus I want him tested on the public school's dime.

I suspect math might be where he's going to have trouble fitting in at public school. (Supporting evidence: He just interrupted my typing to ask me "What's 4 x 4 + 4?" So yeah, mathy!) But if he gets the same teacher DS7 had for K, then I know he'll be fine. She was good!

Finally, I'm still not sure how well I would do as DS4's teacher. His personality is a lot more challenging for me. I don't think it would be easy on either of us. Plus his being an extrovert who needs a lot of people around means that school might really be a better fit in his case.

You know me--I'm going to go with the flow! We'll see how K goes before we make any decisions about 1st grade. DS4 is a very different kid from DS7. I definitely cannot assume that what worked (or didn't work) for one is going to work (or not work) for the other!

Anyway, thanks for asking.

So are you going to HS DS4, too, LMom? Have you made that decision?

Hi Kriston,

Great! I love when that happens.

Have you tried teaching x! (x factorial, as opposed to Hurray for x!) ?

My DS8 asked about it the other night and got very into the idea:

DS8: "Hey, what's this exclamation point on the calculator for?"

<explanation from Mom and other adult>

DS (considering the implications): "Cool!"

The wikipedia has a cool entry on factorials. It has a nifty table with factorial values on the top right. The mathematics below the top part is a bit advanced though.

Val

I used to have summer jobs that involved counting change in the register at the end of the day. I used to count the coins by putting them into pyramids with four coins at the bottom. Each pyramid had 10 coins, and so counting accurately became fast and easy. Other people noticed and starting making pyramids when it was their turn to count change!

I understand your son; I love number tricks like this.

Val

No, Val, we haven't done factorials yet. Good idea! Thanks!

We did do square and triangular numbers earlier this year. That works really well with pattern blocks, actually, and it was one of the things that jumpstarted him on learning his times tables this year. So you'll get a big "YAHOO!" for square and triangular numbers from me!

Heading over to wikipedia now... triangular numbers are new to me....

JB

Oh, you'll LOVE them, JB! The pattern thing will be right up your DS's alley.

Niiice. Get it. First this DW asked about was the relationship to square. Nice.

Now we just need ONE NIGHT where both younin's sleep well.

JB

I too am learning new things (not math that would take a while) but there are things in CyberEd I didn't known about or remember them anymore. BTW play-doh comes quite handy when explaining how mountains, canyons, plateau etc. are created.


Good to hear that things are working out. I hear you on DH not being home, lots of business trips here lately


I think as long as a big chunk of school time is spent by learning new things (reading and writing) then he will be fine. Plus you have a half day K. Can you ask for the same teacher?


I hear you, DS4 is very different from DS6. He is quite a clown but also very stubborn. He does anything and everything to get his way. He has been like that since I can remember. I am sure we would run into problems like we run into problems with DS6 except they would be quite different and it would be like starting from the beginning.


We haven't really talked about that but I believe it's what both DH and I expect at this point. I don't want to make any plans for next year, we all know how it works with gt kids. What I plan now may be useless a few months down the road. One thing is sure, DS4 would be a huge misfit in K. He reads really well now and lately he is just going through what I call an academic spurt. He is not as mathy as his brother was at this age, but he is the kid who needs to know how everything works and loves to make connection between different information. You know the engineering type May be we can compare notes one day. You tell me what DS7 liked and I will use it for DS4 and vice verse

BTW If you teach n! include a lesson about permutations as well. He will love it. It would go nicely with how fast 2 grows when you start doubling it.

Good help! Thanks, LMom!

Yes, we should definitely compare engineering notes. Have you discovered "How It's Made" on the Science Channel yet? DS7 LOVED that show for a while. He could talk for hours about how golf balls and streetlights were made. It's boring as sin to a non-engineer, but DS7 and DH (the engineer) could watch it for hours almost without blinking! LOL!

Of course, "Mythbusters" on the Discovery Channel is also great, even for me. I love those nerds!

Have you given your DS broken appliances and let him tear them apart to see the inside? That's always a hit for engineer-y kids. My dad used to take two broken appliances, crack them open, and create one that worked. A skill I wish I had...

LOL! Like a toast-blender?

We'll see, but some of the things you have been discussing were never "there" in the first place, so they won't be able to come back! (i suppose you'll be telling me there are octagonal numbers, too...) I'm sure DS4 will be telling me soon "i think [insert any name here] knows way more about math [or insert any other topic] than you do."

Oh, and I had to look up heuristics too.

well, humph!

I did, too, the first time I came across the word in teaching lingo, SPG. No worries there. Some of it is just experience with teaching materials.

I learned about triangular numbers from a "math with pattern blocks" book that I bought for this school year. I had never heard of them before that. Haven't we all made pyramids out of stuff before though? The concept is there, even if the terminology isn't.

I'm telling you, you're ahead of the game! Your child is three years younger than mine, and you know as much as I know on this subject already! So much comes out of the learning materials you find...

Oh, and from this forum, of course!

And now I'm off to look at that octagonal numbers link. I've never heard of those...

Thanks for the recommendations. I just told our TiVo about it

We're a big "How's It Made" and Mythbusters household!!! In fact it's where DS8 learned to use the word "d&*n^" thanks again Adam. Ha Ha Ha.

Yes, I do wish they wouldn't curse. But I'm willing to overlook it since it's such a great show otherwise. We just use it as a teachable moment to talk about appropriate and inappropriate language.

Plus, I confess, it's not like my kids have never heard me slip before...